I have the Taylor series of cosh $$\sum_{n=0}^\infty \frac {x^{2n}} {(2n)!}$$

and I know that this series converges for all x, but now I want to know if the series represents the function, in other words, that the function is analytic in that interval. To do so, I should prove that the error term of the taylor expansion of cosh converges to zero, but I can't get the expression of this term.

Thanks for your help!

  • $\begingroup$ It actually converges on the entire complex plane. $\endgroup$ – J.R. Feb 15 '14 at 19:31

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